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Mobius transform of A051664, the number of nonzero terms in the n-th cyclotomic polynomial.
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%I #6 Mar 30 2012 18:37:43

%S 2,0,1,0,3,0,5,0,0,0,9,0,11,0,1,0,15,0,17,0,1,0,21,0,0,0,0,0,27,0,29,

%T 0,3,0,7,0,35,0,3,0,39,0,41,0,0,0,45,0,0,0,5,0,51,0,3,0,5,0,57,0,59,0,

%U 0,0,15,0,65,0,7,0,69,0,71,0,0,0,15,0,77,0,0,0,81,0,21,0,9,0,87,0,5,0,9,0,9

%N Mobius transform of A051664, the number of nonzero terms in the n-th cyclotomic polynomial.

%C Note that a(n) = 0 for even n and a(n) = n-2 for prime n. It appears that the following are true: a(1) is the only positive even term, all odd numbers eventually appear in the sequence, a(n) = 0 if n is squareful and a(n) > 0 if n is squarefree. Assuming the truth of the last statement, we can show that if distinct odd primes p and q divide n, then A051664(n) > p + q - 2.

%H T. D. Noe, <a href="/A087073/b087073.txt">Table of n, a(n) for n=1..1000</a>

%F a(n) = Sum{d|n} mu(n/d) A051664(d)

%Y Cf. A051664.

%K nonn

%O 1,1

%A _T. D. Noe_, Aug 08 2003

%E Definition corrected: "inverse moebius transform" to "moebius transform" by _Wouter Meeussen_, Jan 17 2009